Upcoming Event: Oden Institute Distinguished Lecture

Analysis of Bent Optical Fibers - In memory of Prof. Ivo Babuška

Leszek Demkowicz, Oden Institute, The University of Texas at Austin

Abstract

I will give a comprehensive review of our work on bent optical fibers. Standard (straight) optical fibers experience minimal losses, so that signals can be propagated over long distances without the need for amplification. The situation changes when you bend the fiber (e.g. when you spool it). Physics is reflected with the mathematics, contrary to the straight fiber, the modal eigenvalue problem for the bent fiber involves a non self-adjoint operator.

The reliable determination of losses in bent fibers has been a long standing challenge. It is sufficient to mention that the losses reported in the literature differ by 2-3 orders of magnitude. The mode-dependent losses affect several nonlinear phenomena of interest including Transverse Mode Instability (TMI) that we have successfully stimulated for straight fibers. 

I will report on the analysis of bent optical fibers in my group. 

The work includes:

1. A semianalytical method to compute the losses in slab circular waveguides (2D), based on the solution of a Bessel eigenvalue problem (with J. Mora-Paz, Ch. Taylor, S. Henneking and J. Grosek);

2. A well-posedness and stability analysis of circular waveguides (with M. Halla and M. Melenk);

3. 3D simulations of bent step index fibers using the DPG method and hp3D code (with J. Mora-Paz, S. Henneking and J. Grosek).

Biography